, in which the winning-sets are the minimal sets touching each winning-set in the original game. For example, if in the original game the winning-sets are { {1,2,3},{4,5,6} } then in the dual game they are { {1,4}, {1,5}, {1,6}, {2,4}, {2,5}, {2,6}, {3,4}, {3,5}, {3,6} }. Then, the winning strategies for Breaker playing first on are exactly the winning-strategies for Maker playing first on . Computational Complexity Maker-Breaker game is PSPACE-complete even if the size of each set is restricted to 6. The first result was from 1978 where the size of each set was restricted to 11, where the game was mentioned as (POS CNF 11). Strategies Several kinds of strategies are commonly used to solve Maker-Breaker games. Pairing Strategies In some games, it is possible to partition the elements of X (or a subset of them) into a set of pairwise-disjoint pairs. Under certain conditions, a player can win using the following greedy strategy: "whenever your opponent picks an element of pair i, pick the other element of pair i". The "certain conditions" are different for Maker and for Breaker; see pairing strategy. Strategies from strong positional games Every winning-strategy for First in a strong positional game, is also a winning strategy for Maker in the maker-breaker variant (see Strong positional game#Comparison to Maker-Breaker game). In particular, if in the strong-positional variant there can be no draw, then in the maker-breaker variant Maker has a winning strategy. The opposite is not necessarily true: a winning-strategy for Maker in the maker-breaker variant is not necessarily a winning-strategy for First in the strong variant, since in the strong variant, Second can win by claiming a winning-set before First. In contrast, every winning-strategy for Breaker in a maker-breaker game, is also a drawing-strategy for Second in the strong-positional variant. Potential-based strategies Suppose we can find a function that assigns, to each winning-set, a potential based on the number of elements already taken from it by Maker/Breaker. The potential function should satisfy the following properties: The potential of a winning-set is between 0 and 1; When Breaker takes an element, the potential of all sets containing it drops to 0 and remains 0; When Maker takes an element, the potential of all (non-broken) sets containing it increases; The potential of a set owned by Maker is 1. Then, Maker wins iff the potential-sum is more than 0, and Breaker wins iff